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3 years ago

Solve the given equation. 5^(1/4)/125^(x/3) =1

Mathematics

1 answer:

scZoUnD [109]3 years ago

3 0

Answer:

x = 0.25

Step-by-step explanation:

Rewrite the equation as:

$\frac{\sqrt[4]{5}}{125^{x/3}} = 1$

$\sqrt[4]{5} = 125^{x/3}$

$(\sqrt[4]{5})^4 = (125^{x/3})^4$

$5 = 125^{4x/3}$

$ln5 = ln(125^{4x/3})$

$ln5 = \frac{4x}{3}ln125$

$x = \frac{3}{4}\frac{ln5}{ln125} = \frac{3}{4}\frac{1}{3} = \frac{1}{4} = 0.25$

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Read 2 more answers

If P = Set of all triangles, Q = Set of scalene triangles, R = Set of isosceles triangles and

Mashutka [201]

Given:

P = Set of all triangles,

Q = Set of scalene triangles,

R = Set of isosceles triangles and

S = Set of equilateral triangles.

To find:

Which of the following statements are true or false?

Solution:

We know that,

Scalene triangles : All sides are different.

Isosceles triangles : Two sides are equal.

equilateral triangles : All sides are equal.

Set of all triangles contains all scalene triangles. So, set of scalene triangles Q is a subset of Set of all triangles P.

$Q\subset P$

So, (a) is true.

All isosceles triangles are not equilateral triangles. So, set of isosceles triangles R is not a subset of set of equilateral triangles S.

$R\nsubseteq S$

So, (b) is false.

Set of all isosceles triangles contains all equilateral triangles. So, set of equilateral triangles S is a subset of set of isosceles triangles R .

$S\subset R$

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3 years ago

A triangle has two sides of length 1 and 2. What compound inequality describes the possible lengths for the third side, x?Write

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Step-by-step explanation:

since in a triangle each side must be shorter than the sum of the other 2 sides (otherwise the end points cannot connect, and there is no triangle), the necessary inequality condition must be

side < 1 + 2 = 3

so,

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for a lower limit let's go through the cases

1 < 2 + side (is always true)

2 < 1 + side

1 < side (side must be larger than 1)

and again

side < 1 + 2 = 3

side < 3

so the full restriction for the third side is

1 < side < 3

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3 years ago

A rectangle has a height of b3 + b2 and a width of b2 + 76 + 4.

zaharov [31]

Answer:

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Step-by-step explanation:

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$a = ({x}^{ 3} + {x}^{2} )( {x}^{2} + 7x + 4) \\ a = {x}^{5} + 7{x}^{4} + 4 {x}^{3} \\ + {x}^{4} + 7 {x}^{3} + 4 {x}^{2} \\ a = {x}^{5} + 8 {x}^{4} + 11 {x}^{3} + 4 {x}^{2}$

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